Rachel the robot is exploring an alien planet. Her computer brain keeps track of the world around her in terms of $x$ and $y$ coordinates (see graph below).
Rachel is running low on battery. She wants to collect a rock sample before returning to her charging station, but she is worried this may cause her to run out of battery.
**How much shorter would it be for Rachel to go straight to her charging station than for her to collect the rock along the way?**
[[☃ input-number 1]] $\text{m}$
Round your *final answer* to the nearest tenth of a meter. Do not round intermediate calculations.
*Coordinate values are in meters.*